Mild-mannered pensioner Harold Fry (Jim Broadbent) takes a stroll to the postbox one bright Devon morning. But for some reason he can’t bring himself to post the letter. It’s just a few stunted lines on headed notepaper, a reply to his old friend and former work colleague Queenie (Linda Bassett), who, he learned recently, has terminal cancer. Then a chance encounter in a petrol station gives Harold a new purpose: he decides to walk from Devon to Berwick-upon-Tweed, where Queenie is receiving palliative care in a hospice. It’s an act of faith: he believes that by plodding through the B-roads of rural Britain he can save her life. His wife, Maureen (Penelope Wilton), hurt and confused by her husband’s abandonment, vacuums despondently.

Initially, this autumn-years road movie, which was adapted by Rachel Joyce from her own novel, chugs along amiably, a cosily familiar tale of British eccentricity. But as a blistered and weathered Harold limps into the film’s heart-sore third act, director Hettie Macdonald, whose TV work includes Normal People, shifts up an emotional gear or two. This politely unassuming little film builds into a wrenching examination of grief, guilt and eventual closure.

• The Unlikely Pilgrimage of Harold Fry is out in cinemas in the UK now and on 8 June in Australia.